相关论文: Crossing Probabilities and Modular Forms
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
We construct general models for holographic superconductivity parametrized by three couplings which are functions of a real scalar field and show that under general assumptions they describe superconducting phase transitions. While some…
We establish the functional relations between generating series of higher-order free cumulants and moments in higher-order free probability, solving an open problem posed fifteen years ago by Collins, Mingo, \'Sniady and Speicher. We…
Molecular search phenomena are observed in a variety of chemical and biological systems. During the search the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic…
We experimentally and numerically investigate the clogging behavior of granular materials in a two-dimensional vertical pipe. The nonmonotonicity of clogging probability found in a cylindrical vertical pipe [L\'opez et al., Phys. Rev. E…
The free energies of the conformal field theories dual to charged adS and rotating adS black holes show Hawking-Page phase transition. We study the transition by constructing boundary free energies in terms of order parameters. This is done…
Rotating turbulence is an example of a three-dimensional system in which an inverse cascade of energy, from the small to the large scales, can be formed. While usually understood as a byproduct of the typical bidimensionalization of…
Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often…
We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
We re-examine a population model which exhibits a continuous absorbing phase transition which belongs to directed percolation in 1+1 dimensions and a first order transition in 2+1 dimensions and above. Studying the model on fractal…
We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…
We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field…
We consider directed polymers in 1+1 spatial dimension under action of an external repulsive potential along a line. Using the exact mapping onto imaginary time evolution of free fermions we find that for sufficiently strong potential the…
A useful result about leftmost and rightmost paths in two dimensional bond percolation is proved. This result was introduced without proof in \cite{G} in the context of the contact process in continuous time. As discussed here, it also…
Applying the "Complexity=Action" conjecture, we study the holographic complexity close to crossover/phase transition in a holographic QCD model proposed by Gubser et al. This model can realize three types of phase transition, crossover or…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…